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3 years ago

Which of the following is the sum of 1/2 and -2/3

Mathematics

1 answer:

Lilit [14]3 years ago

4 0

Answer:

- 1/6

Step-by-step explanation:

find the common denominators 3/6 - 4/6 = - 1/6

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The school that Emily goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold24 adult tic

qwelly [4]

Answer:

Step-by-step explanation:

Let x represent the price of one adult ticket.

Let y represent the price of one student ticket.

On the first day of ticket sales the school sold 24 adult tickets and 3 student tickets for a total of $223.00. This means that

24x + 3y = 223 - - - - - - - - - - - -1

The school took in $152 on the second day by selling 7 adult tickets and 6 student tickets. This means that

7x + 6y = 152 - - - - - - - - - - - - - -2

Multiplying equation 1 by 6 and equation 2 by 3, it becomes

144x + 18y = 1338

21x + 18y = 456

Subtracting, it becomes

123x = 882

x = 882/123

x = 7.17

Substituting x = 7.17 into equation 2, it becomes

7 × 7.17 + 6y = 152

50.19 + 6y = 152

6y = 152 - 50.19 = 101.81

y = 101.81/6 = 16.97

3 0

3 years ago

Use rhombus ABCD and the given information to find each value.

Semmy [17]

Answer: (c) 31 (d) 30 (e) 41 (f) 10

<u>Step-by-step explanation:</u>

NOTES about angles of a rhombus:

diagonals are angle bisectors (cut the angle into 2 equal parts)
diagonals are perpendicular to each other (90°)
two adjacent triangles of a rhombus form an isosceles triangle

Per rule 2 → ∠BEC = 90°

Triangle Sum Theorem: sum of the angles of a triangle = 180°

∠CBD + ∠BEC + ∠BCE = 180°

59° + 90° + ∠BCE = 180°

149° + ∠BCE = 180°

∠BCE = 31°

(d) Given: ∠BCD = 120°

Per rule 3 → ∠CBD = ∠CDB

Triangle Sum Theorem: sum of the angles of a triangle = 180°

∠CBD + ∠CDB + ∠BCD = 180°

2∠CBD + 120° = 180°

2∠CBD = 60°

∠CBD = 30°

(e) Given: ∠AED = 2x+8

Per rule 2 → ∠AED = 90°

2x+8 = 90

2x = 82

x = 41

(f) Given: ∠BCE = 3x + 3 and ∠ECD = 5x - 17

Per rule 1 → ∠BCE = ∠ECD

3x + 3 = 5x- 17

3 = 2x - 17

20 = 2x

10 = x

4 0

3 years ago

Use the quadratic formula to solve 5x^2+2x-3

Lisa [10]

Assuming it equals 0
for
ax^2+bx+c=0
x= $\frac{-b+/- \sqrt{b^2-4ac} }{2a}$

given
5x^2+2x-3=0
a=5
b=2
c=-3

x= $\frac{-2+/- \sqrt{2^2-4(5)(-3)} }{2(5)}$
x= $\frac{-2+/- \sqrt{4+60} }{10}$
x= $\frac{-2+/- \sqrt{64} }{10}$
x= $\frac{-2+/- 8 }{10}$
x=(-2+8)/10 or (-2-8)/10
x=6/10 or -10/10
x=3/5 or -1

6 0

3 years ago

The variable z is directly proportional to x, and inversely proportional to y. When x is 9 and y is 6, z has the value 19.5. Wha

Pavel [41]

Given that, the variable z is directly proportional to x, and inversely proportional to y.

So, we can set up an equation as following:

$z= k \frac{x}{y}$ Where k = constant of variation.